Permutations and Combinations: practice questions

6 questions · 11 marks · free, no account · Read the notes first

1. Question 1Multiple choice · 1 mark

   In how many ways can the letters of the word STUDY be arranged in a row?

   A

   $25$

   B

   $60$

   C

   $120$

   D

   $5$

2. Question 2Multiple choice · 1 mark

   In how many ways can a committee of 3 be chosen from 8 students?

   A

   $336$

   B

   $56$

   C

   $24$

   D

   $512$

3. Question 3Multiple choice · 1 mark

   5 boys and 3 girls stand in a row. In how many ways can they stand if the 3 girls must be next to each other?

   A

   $720$

   B

   $40\,320$

   C

   $2160$

   D

   $4320$

4. Question 4Multiple choice · 1 mark

   How many 4-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if no digit is repeated?

   A

   $180$

   B

   $360$

   C

   $120$

   D

   $90$

5. Question 53 marks

   A committee of 4 is to be formed from 6 boys and 5 girls. In how many ways can this be done if the committee must have at least 1 girl?

   Show worked solution

   Total number of committees $= C^{11}_4 = 330$ 1A

   Committees with no girls $= C^6_4 = 15$ 1A

   Required number $= 330 - 15 = 315$ 1A

6. Question 64 marks

   7 people, including Amy and Ben, stand in a row. In how many ways can they stand if Amy and Ben must not stand next to each other?

   Show worked solution

   Total number of arrangements $= 7! = 5040$ 1A

   Amy and Ben next to each other $= 6! \times 2!$ 1M

   $= 1440$ 1A

   Required number $= 5040 - 1440 = 3600$ 1A